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Concepts and reason Statistical hypotheses testing: Hypotheses testing is used to make inferences about the population based on the sample data. The hypotheses test consists of null hypothesis and alternative hypothesis. Null hypothesis: The null hypothesis states that there is no difference in the test, which is denoted by {H_0} H 0 . Moreover, the sign of null hypothesis is equal left( = right) (=) , greater than or equal left( ge right) (≥) and less than or equal left( le right) (≤) . Alternative hypothesis: The hypothesis that differs from {H_0} H 0 is called alternative hypothesis. This signifies that there is a significant difference in the test. The sign of alternative hypothesis is less than left( < right) ( right) (>) , or not equal left( ne right) (≠) . Proportion: The ratio of the number of favorable outcomes and total number of possible outcomes in the sample called as the proportion. Z-statistic for proportion: The standardized z- statistic is defined as the ratio of the ‘distance of the observed statistic from the proportion of the null distribution’ and the ‘standard deviation of the null distribution’. P-value: The probability of getting the value of the statistic that is as extreme as the observed statistic when the null hypothesis is true is called as P-value. Therefore, it assumes “null hypothesis is true”. Fundamentals The formula for sample proportion is, {rm{Sample proportion}}left( {hat p} right) = frac{x}{n} Sampleproportion( p ^ )= n x Where x is the number of success in the sample and n is the total sample size. The formula for population proportion is, {rm{Population proportion}}left( {{p_0}} right) = frac{X}{N} Populationproportion(p 0 )= N X Where X is the number of success in the population and N is the total population size. The test statistic for one proportion is, z = frac{{hat p - {p_0}}}{{sqrt {frac{{{p_0}left( {1 - {p_0}} right)}}{n}} }} z= n p 0 (1−p 0 ) p ^ −p 0 Here, begin{array}{c}\hat p:{rm{Sample}},{rm{proportion}}\\{p_0}:{rm{Population}},{rm{proportion}}\\n:{rm{Sample}},{rm{size}}\end{array} p ^ :Sampleproportion p 0 :Populationproportion n:Samplesize The formula for the p-value for right-sided test is, p{rm{ - value}} = Pleft( {Z > z} right) p−value=P(Z>z) Procedure for finding the probability is listed below: 1.From the table of standard normal distribution, locate the z-value 2.Move left until the first column is reached. 3.Move upward until the top row is reached. 4.Locate the probability value, by the intersection of the row and column values gives the area to the left of z.
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